They're living in the homes of people who want a nanny without paying minimum wage.

Illegal immigrants go home when there's no work to be done. Clamp down on employers and problem is solved. But that means you don't get cheap babysitters, maids, landscapers, etc. that you pay under the table, and it means your bill at hotels and restaurants go up as housekeepers, dishwashers and other staff are paid legally. It also means your produce prices go up.

America loves the benefits of illegal labor, just not the costs.

And "real Americans" can't do this work. Have you seen your average Walmart shopper? Put that in a field to harvest for 12 hours. They'd die.